In 3D computer graphics, 3D modeling is the process of developing a mathematical representation of any 3D surface of object (either inanimate or living) via specialized software. The resulting product is called a 3D model, which represents a 3D object using a collection of points in 3D space, connected by various geometric entities such as triangles, lines, curved surface, etc. Being a collection of data (points and other information), 3D models can be created manually, algorithmically (procedural modeling), or scanned.
Shape understanding has been an intensive research topic in computer vision and graphics. For 3D models, it is crucial to understand the structures in many applications, such as modeling, compression, animation, editing, synthesis, etc. Generally, the high-level representation of a 3D model can capture the functionality and regularity in the organization of its components. Such a high-level representation can be depicted as a skeleton model, a tree representation or a graph model, etc.
For most of man-made 3D objects, symmetry and hierarchical structures usually exist. In previous work, the two characteristics have been combined to construct the high-level representation. In Y. Wang, K. Xu, J. Li, H. Zhang, A. Shamir, L. Liu, Z. Cheng, Y. Xiong. Symmetry Hierarchy of Man-Made Objects Computer Graphics Forum (Eurographics 2010), vol. 30, no. 2, pp. 287-296, 2011, it introduces symmetry hierarchy of man-made objects, which provides a symmetry-induced, hierarchical organization of the model's constituent parts. This work uses a 3D mesh as input and returns a tree representation, whose leaf nodes are the constituent parts of the 3D mesh and the internal nodes represent symmetry-grouping or part-assembly operations.
Although the symmetry hierarchy method performs well on the prerequisite excellent symmetry results, it is challenging to segment the input model for symmetry discovery. Due to missing data and noise, the symmetry detection sometimes generates a few false results. In addition, the high-level representation is built on the user-defined criteria, which are concluded based on observations.